Transporting the Transporter

I've never seen an episode that might deal with this maybe someone else has.

Can a transporter transport itself? If the power unit was part of the transporter; it should in theory be (trek universe) possible. Right?

If it could it would be a new way to travel in space. You could even use two or more transporters joined together; while in the matter stream the other transporter(s) transported the matter stream further out...each transporter taking a turn to transport themselves and/or matter streams further and further out in into space until resolution peaks then consolidate all beams.